Recreational Mathematics · Prime Numbers

Fixed-Digit Repetition Prime Patterns Generator

Created by Inder J. Taneja

Choose a prime seed and a fixed digit block. Insert one, then two, then three copies of that same block at the chosen position. For a seed AB, the sequence is AB → A(k)B → A(kk)B → A(kkk)B. The whole block is repeated; its individual digits may repeat.

Choose the search

A 1d range of 1–9 tests 9 blocks; a 2d range of 10–99 tests 90 blocks. For 3d–9d, the suggested starting range contains 100 blocks; widen it as needed. Set Block from and Block to to the same number to test one block. Leading zeros are allowed: enter 7–7 with 2d to test 07. At the front, an inserted number must not begin with 0.

Insertion position
Prime run

“Exactly” verifies that the next insertion is composite. “At least” continues through the prime run and then shows its first composite term separately (up to 30 prime terms).

Output

Downloads include every result found in the completed search, even when fewer cards are shown.

Prime patterns

0 patterns tested0 resultsReady
The starting seed is prime. For numbers below 2⁶⁴, the primality check is deterministic; larger numbers are labelled probable primes.
Choose the block length, insertion position, and prime run to begin.

References

This work is based on the author’s following research:

  1. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Lengths 10, 9 and 8, Zenodo, February 8, 2019, pp. 1–175. doi:10.5281/zenodo.2560640 ↗
  2. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 7, Zenodo, February 8, 2019, pp. 1–176. doi:10.5281/zenodo.2560668 ↗
  3. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 6, Zenodo, February 9, 2019, pp. 1–303. doi:10.5281/zenodo.2561096 ↗
  4. Inder J. Taneja, Prime Numbers in Fixed Digits Repetitions Prime Patterns, Zenodo, November 10, 2020, pp. 1–280. doi:10.5281/zenodo.4265818 ↗
  5. Inder J. Taneja, 4-Digits Prime Numbers in Fixed Digits Repetition Prime Patterns, Zenodo, November 29, 2020, pp. 1–1544. doi:10.5281/zenodo.4295652 ↗
  6. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns for 5-Digits Prime Numbers, Zenodo, January 17, 2021, pp. 1–2069. doi:10.5281/zenodo.4445395 ↗

Previous works of the author

  1. Inder J. Taneja, Patterns in Prime Numbers: Fixed Digits Repetitions, RGMIA Research Report Collection, 20 (2017), Art. 17, pp. 1–75. RGMIA PDF ↗
  2. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – I, RGMIA Research Report Collection, 20 (2017), Art. 73, pp. 1–104. RGMIA PDF ↗
  3. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – II, RGMIA Research Report Collection, 20 (2017), Art. 74, pp. 1–109. RGMIA PDF ↗
  4. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – III, RGMIA Research Report Collection, 20 (2017), Art. 93, pp. 1–113. RGMIA PDF ↗
  5. Inder J. Taneja, Multiple Choice Patterns in Prime Numbers – IV, RGMIA Research Report Collection, 20 (2017), Art. 94, pp. 1–150. RGMIA PDF ↗
  6. Inder J. Taneja, Patterns in Prime Numbers: Fixed Digits Repetitions, February 23, 2017. WordPress article ↗